4 citations · 4 across the 8 of their papers we have counts for
8 papers · 1 filter
Fourier Decay of SRB Measures for Skew Products
Gaétan Leclerc, Haojie Ren
We study Fourier decay of natural invariant measures for real analytic skew products on , where is expanding and $0<|\partial…
Fourier decay of equilibrium states and the Fibonacci Hamiltonian
Gaétan Leclerc
We show power Fourier decay for equilibrium states of nonlinear, area preserving, smooth Axiom-A diffeomorphisms on surfaces. This implies positivity of the lower Fourier dimension…
Fourier decay in parabolic systems with overlaps
Gaétan Leclerc, Sampo Paukkonen, Tuomas Sahlsten
We establish power Fourier decay for equilibrium states of parabolic iterated function systems with overlaps satisfying a multiscale nonlinearity condition. This class in…
Nonlinearity, Fractals, Fourier decay -- Harmonic analysis of equilibrium states for hyperbolic dynamical systems
Gaétan Leclerc
This is my (reviewed) PhD manuscript. It contains 6 Chapters, which contains mostly already published work, except for Chapter 5 which is new. Chapter 1 introduce basic notions on…
Fourier decay of equilibrium states on hyperbolic surfaces
Gaétan Leclerc
Let be a (convex-)cocompact group of isometries of the hyperbolic space , let be the associated hyperbolic manifold, and consider a real val…
Fourier decay of equilibrium states for bunched attractors
Gaétan Leclerc
Let be a closed manifold, and let be a Axiom A diffeomorphism. Suppose that has an attractor with codimension 1 stable lamination. Under a…
On oscillatory integrals with Hölder phases
Gaétan Leclerc
We exhibit a family of autosimilar Hölder maps that satisfies a fractal version of the Van Der Corput Lemma, despite not being absolutely continuous. The result is a direct consequ…
Julia sets of hyperbolic rational maps have positive Fourier dimension
Gaétan Leclerc
Let be a hyperbolic rational map of degree , and let be its Julia set. We prove that a…